Midterm Homework - Application of Financial Software
Bat-Erdene Zorigtbaatar
2026-04-14
Chapter 2
Basic Data Exploration (Auto Dataset)
data(Auto)
glimpse(Auto)## Rows: 392
## Columns: 9
## $ mpg <dbl> 18, 15, 18, 16, 17, 15, 14, 14, 14, 15, 15, 14, 15, 14, 2…
## $ cylinders <int> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 6, 6, 6, 4, …
## $ displacement <dbl> 307, 350, 318, 304, 302, 429, 454, 440, 455, 390, 383, 34…
## $ horsepower <int> 130, 165, 150, 150, 140, 198, 220, 215, 225, 190, 170, 16…
## $ weight <int> 3504, 3693, 3436, 3433, 3449, 4341, 4354, 4312, 4425, 385…
## $ acceleration <dbl> 12.0, 11.5, 11.0, 12.0, 10.5, 10.0, 9.0, 8.5, 10.0, 8.5, …
## $ year <int> 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 7…
## $ origin <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, …
## $ name <fct> chevrolet chevelle malibu, buick skylark 320, plymouth sa…summary(Auto)## mpg cylinders displacement horsepower weight
## Min. : 9.00 Min. :3.000 Min. : 68.0 Min. : 46.0 Min. :1613
## 1st Qu.:17.00 1st Qu.:4.000 1st Qu.:105.0 1st Qu.: 75.0 1st Qu.:2225
## Median :22.75 Median :4.000 Median :151.0 Median : 93.5 Median :2804
## Mean :23.45 Mean :5.472 Mean :194.4 Mean :104.5 Mean :2978
## 3rd Qu.:29.00 3rd Qu.:8.000 3rd Qu.:275.8 3rd Qu.:126.0 3rd Qu.:3615
## Max. :46.60 Max. :8.000 Max. :455.0 Max. :230.0 Max. :5140
##
## acceleration year origin name
## Min. : 8.00 Min. :70.00 Min. :1.000 amc matador : 5
## 1st Qu.:13.78 1st Qu.:73.00 1st Qu.:1.000 ford pinto : 5
## Median :15.50 Median :76.00 Median :1.000 toyota corolla : 5
## Mean :15.54 Mean :75.98 Mean :1.577 amc gremlin : 4
## 3rd Qu.:17.02 3rd Qu.:79.00 3rd Qu.:2.000 amc hornet : 4
## Max. :24.80 Max. :82.00 Max. :3.000 chevrolet chevette: 4
## (Other) :365Relationship between mpg and horsepower
ggplot(Auto, aes(x = horsepower, y = mpg)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) +
labs(title = "MPG vs Horsepower")## `geom_smooth()` using formula = 'y ~ x'
Interpretation
There is a clear negative relationship between horsepower and fuel efficiency.
Chapter 3: Linear Regression
Simple Linear Regression
lm_fit <- lm(mpg ~ horsepower, data = Auto)
summary(lm_fit)##
## Call:
## lm(formula = mpg ~ horsepower, data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.5710 -3.2592 -0.3435 2.7630 16.9240
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.935861 0.717499 55.66 <2e-16 ***
## horsepower -0.157845 0.006446 -24.49 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.906 on 390 degrees of freedom
## Multiple R-squared: 0.6059, Adjusted R-squared: 0.6049
## F-statistic: 599.7 on 1 and 390 DF, p-value: < 2.2e-16Predictions
predict(lm_fit, newdata = tibble(horsepower = c(100,150)))## 1 2
## 24.15139 16.25915Multiple Linear Regression
lm_multi <- lm(mpg ~ cylinders + displacement + horsepower + weight + acceleration + year + origin,
data = Auto)
summary(lm_multi)##
## Call:
## lm(formula = mpg ~ cylinders + displacement + horsepower + weight +
## acceleration + year + origin, data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5903 -2.1565 -0.1169 1.8690 13.0604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.218435 4.644294 -3.707 0.00024 ***
## cylinders -0.493376 0.323282 -1.526 0.12780
## displacement 0.019896 0.007515 2.647 0.00844 **
## horsepower -0.016951 0.013787 -1.230 0.21963
## weight -0.006474 0.000652 -9.929 < 2e-16 ***
## acceleration 0.080576 0.098845 0.815 0.41548
## year 0.750773 0.050973 14.729 < 2e-16 ***
## origin 1.426141 0.278136 5.127 4.67e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.328 on 384 degrees of freedom
## Multiple R-squared: 0.8215, Adjusted R-squared: 0.8182
## F-statistic: 252.4 on 7 and 384 DF, p-value: < 2.2e-16Diagnostic Plots
par(mfrow = c(2,2))
plot(lm_multi)
Interpretation
- Several predictors are statistically significant
- Residual plots indicate possible non-linearity
Chapter 4: Classification
Default Dataset
data(Default)
Default <- Default %>%
mutate(default = as.factor(default),
student = as.factor(student))Logistic Regression Models
Model 1: balance
model1 <- glm(default ~ balance, data = Default, family = binomial)
summary(model1)##
## Call:
## glm(formula = default ~ balance, family = binomial, data = Default)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.065e+01 3.612e-01 -29.49 <2e-16 ***
## balance 5.499e-03 2.204e-04 24.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2920.6 on 9999 degrees of freedom
## Residual deviance: 1596.5 on 9998 degrees of freedom
## AIC: 1600.5
##
## Number of Fisher Scoring iterations: 8Model 2: income
model2 <- glm(default ~ income, data = Default, family = binomial)
summary(model2)##
## Call:
## glm(formula = default ~ income, family = binomial, data = Default)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.094e+00 1.463e-01 -21.156 <2e-16 ***
## income -8.353e-06 4.207e-06 -1.985 0.0471 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2920.6 on 9999 degrees of freedom
## Residual deviance: 2916.7 on 9998 degrees of freedom
## AIC: 2920.7
##
## Number of Fisher Scoring iterations: 6Model 3: full model
model3 <- glm(default ~ balance + income + student,
data = Default,
family = binomial)
summary(model3)##
## Call:
## glm(formula = default ~ balance + income + student, family = binomial,
## data = Default)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.087e+01 4.923e-01 -22.080 < 2e-16 ***
## balance 5.737e-03 2.319e-04 24.738 < 2e-16 ***
## income 3.033e-06 8.203e-06 0.370 0.71152
## studentYes -6.468e-01 2.363e-01 -2.738 0.00619 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2920.6 on 9999 degrees of freedom
## Residual deviance: 1571.5 on 9996 degrees of freedom
## AIC: 1579.5
##
## Number of Fisher Scoring iterations: 8Predictions
prob <- predict(model3, type = "response")
pred_class <- ifelse(prob > 0.5, "Yes", "No") %>%
factor(levels = c("No","Yes"))Confusion Matrix
conf_mat(data.frame(truth = Default$default,
pred = pred_class),
truth = truth,
estimate = pred)## Truth
## Prediction No Yes
## No 9627 228
## Yes 40 105ROC Curve
roc_obj <- roc(Default$default, prob)## Setting levels: control = No, case = Yes## Setting direction: controls < casesplot(roc_obj, col = "blue", main = "ROC Curve")
auc(roc_obj)## Area under the curve: 0.9496Interpretation
- Balance is the strongest predictor of default
- Logistic regression performs well (high AUC)
- Income contributes little explanatory power
Final Conclusion
This Midterm applied statistical learning methods across multiple domains:
- Chapter 2 explored data relationships
- Chapter 3 applied linear regression models
- Chapter 4 focused on classification using logistic regression
The results highlight the importance of selecting relevant predictors and evaluating model performance using both statistical and graphical methods.